Question: The grades on a language midterm at Covington are normally distributed with $\mu = 73$ and $\sigma = 3.5$. William earned a n $80$ on the exam. Find the z-score for William's exam grade. Round to two decimal places.
Explanation: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for William's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{80 - {73}}{{3.5}}} $ ${ z \approx 2.00}$ The z-score is $2.00$. In other words, William's score was $2.00$ standard deviations above the mean.